Method for determining a curved laying track of each layer of a composite material laminate

Abstract

The application belongs to the technical field of curve laying track determination of each layer of composite laminated plate, and particularly relates to a curve laying track determination method of each layer of composite laminated plate, comprising the following steps: determining reference laying bands of each layer of the composite laminated plate; assuming that points on each laying band of each layer of the composite laminated plate are equidistant from the center line of the reference laying band in the normal direction; calculating the laying band and the laying angle of each point in the range of each layer of the composite laminated plate, and then obtaining the curve laying track of each laying band.

Description

Technical Field

[0001] This application belongs to the technical field of composite laminate layer laying curve design, specifically involving a method for determining the laying curve trajectory of each layer of composite laminate. Background Technology

[0002] Composite laminates possess excellent mechanical properties and have wide applications in engineering. Currently, the layers of composite laminates are mostly formed by laying strips side by side in straight lines at equal intervals at a certain angle. This cannot fully utilize the directional characteristics of the composite strips. Therefore, it is necessary to design the laying strips of each layer of composite laminate to be laid in a set curved form. However, since the curvature of each laying strip trajectory is constantly changing, if the laying strips are still laid at equal intervals, the edges of the laying strips will overlap or gaps will exist, resulting in structural defects in the composite laminate and seriously affecting its performance.

[0003] This application is made in view of the aforementioned technical deficiencies.

[0004] It should be noted that the above background information is only used to assist in understanding the inventive concept and technical solution of this invention, and it does not necessarily belong to the prior art of this patent application. In the absence of clear evidence that the above information was disclosed on the filing date of this application, the above background information should not be used to evaluate the novelty and inventiveness of this application. Summary of the Invention

[0005] The purpose of this application is to provide a method for determining the laying trajectory of the laying curve of each layer of a composite laminate, so as to overcome or mitigate at least one of the known technical defects.

[0006] The technical solution of this application is:

[0007] 1. A method for determining the layup trajectory of each layer of a composite laminate, characterized in that it includes:

[0008] Determine the reference layup strips for each layer of the composite laminate;

[0009] Assuming that the points on each layup strip of each layer of the composite laminate are equidistant from the centerline of the reference layup strip in the normal direction, the layup strip and its layup angle of each point within each layer of the composite laminate are calculated, and the curved layup trajectory of each layup strip is obtained.

[0010] According to at least one embodiment of this application, in the above-described method for determining the layup trajectory of each layer of the composite laminate, the determination of the reference layup strip for each layer of the composite laminate specifically involves:

[0011] The composite laminate is laid out according to a set curve, with the centerline passing through the midpoint of each layer as a reference layout strip.

[0012] According to at least one embodiment of this application, in the above-described method for determining the layup trajectory of each layer of the composite laminate, the calculation of the layup zone and its slope at each point within the range of each layer of the composite laminate specifically involves:

[0013]

[0014]

[0015] (x-x0)+(y-y0(x0))tan[θ(x0)]=0;

[0016]

[0017]

[0018] θ(P) = θ(x0);

[0019] in,

[0020] k is the number of the laying strip where the point is located within each layer of the composite laminate;

[0021] floor() is a function that rounds down to the nearest integer.

[0022] d is the distance from a point within each layer of the composite laminate along the normal direction to the centerline of the reference layup strip;

[0023] W max This refers to the maximum width of the laying strip;

[0024] x and y are the coordinates of points within the range of each layer of the composite laminate;

[0025] x0 and y0 are the coordinates of a point on the center line of the reference paving strip;

[0026] θ(x0) is the laying angle of the reference laying strip centerline point;

[0027] a is the length of each layer of the composite laminate along the x-axis;

[0028] T0 is the angle between the centerline of the test layup strip at the midpoint of each layer of the composite laminate and the x-axis;

[0029] T1 is the angle between the centerline of the test layup strip at the edge of each layer of the composite laminate and the x-axis;

[0030] θ(P) is the laying angle of the layup strip where the point is located within each layer of the composite laminate.

[0031] According to at least one embodiment of this application, in the above-mentioned method for determining the layup trajectory of each layer of the composite laminate, (x-x0)+(y-y0(x0))tan[θ(x0)]=0 is solved by the following method:

[0032] make

[0033]

[0034]

[0035] g'(x0)=(y-y0(x0))(1+tan 2 [θ(x0)])θ'(x0)-tan 2 [θ(x0)]-1;

[0036] exist At that time, take

[0037] in,

[0038] Calculate the iteration values ​​for the initial, nth, and (n+1)th iterations of x0;

[0039] λ and μ are random numbers between 0 and 1;

[0040] TOL stands for tolerance.

[0041] According to at least one embodiment of this application, in the above-described method for determining the layup trajectory of each layer of the composite laminate, TOL = 10. -4 .

[0042] This application has at least the following beneficial technical effects:

[0043] A method for determining the curved layup trajectory of each layer of a composite laminate is provided. This method assumes that points on each layup strip of each layer of the composite laminate are equidistant from the centerline of a reference layup strip in the normal direction. Based on this, the layup strip and its layup angle at each point within each layer of the composite laminate are calculated, thereby obtaining the curved layup trajectory of each layup strip. This method designs equidistant layup strips in the normal direction within each layer of the composite laminate, thus avoiding overlap or gaps at the edges of the layup strips during layup and ensuring the performance of the composite laminate. Attached Figure Description

[0044] Figure 1 This is a schematic diagram of the method for determining the layup trajectory of each layer of the composite laminate provided in the embodiments of this application;

[0045] Figure 2This is a schematic diagram of the centerline of the reference laying strip provided in an embodiment of this application;

[0046] Figure 3 This is a schematic diagram of the dimensional relationship of the laying tape provided in the embodiments of this application;

[0047] Figure 4 This is a schematic diagram showing the offset of the centerline of the reference laying strip along the normal direction provided in the embodiments of this application;

[0048] Figure 5 This is a schematic diagram of the curved layup trajectory of each layer of the composite laminate provided in the embodiments of this application.

[0049] To better illustrate this embodiment, some parts in the accompanying drawings may be omitted, enlarged, or reduced, and do not represent the actual size of the product. Furthermore, the accompanying drawings are for illustrative purposes only and should not be construed as limiting this patent. Detailed Implementation

[0050] To make the technical solution and advantages of this application clearer, the technical solution of this application will be described in a clearer and more complete manner below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are only some embodiments of this application, and are only used to explain this application, not to limit this application. It should be noted that, for ease of description, only the parts related to this application are shown in the accompanying drawings. Other related parts can be referred to the general design. In the absence of conflict, the embodiments and technical features in the embodiments of this application can be combined with each other to obtain new embodiments.

[0051] Furthermore, unless otherwise defined, the technical or scientific terms used in this application description shall have the ordinary meaning understood by one of ordinary skill in the art to which this application pertains. The terms "upper," "lower," "left," "right," "center," "vertical," "horizontal," "inner," and "outer," etc., used in this application description to indicate relative direction or positional relationship are used only to indicate relative orientation or positional relationship, and do not imply that the device or component must have a specific orientation, or be constructed and operated in a specific orientation. When the absolute position of the described object changes, its relative positional relationship may also change accordingly, and therefore should not be construed as a limitation on this application. The terms "first," "second," "third," and similar terms used in this application description are used only for descriptive purposes to distinguish different components, and should not be construed as indicating or implying relative importance. The terms "a," "one," or "the," etc., used in this application description should not be construed as an absolute limitation on quantity, but should be construed as indicating the existence of at least one. The terms "including," "comprising," etc., used in this application description mean that the element or object preceding the word covers the element or object listed after the word and its equivalents, without excluding other elements or objects.

[0052] Furthermore, it should be noted that, unless otherwise explicitly specified and limited, terms such as “installation,” “connection,” and “linkage” used in the description of this application should be interpreted broadly. For example, a connection can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium; or it can be a connection within two components. Those skilled in the art can understand its specific meaning in this application according to the specific circumstances.

[0053] The following is in conjunction with the appendix Figures 1 to 5 This application will be described in further detail.

[0054] The reference tile centerline is defined using the linear angle tile method, such as... Figure 2 As shown, a rectangular coordinate system is established at the center point of the composite laminate, with the x-axis horizontal and the y-axis vertical. The angle between the layup tape direction and the x-axis is defined as the layup angle. The angles between the tangent of the curve at the center and boundary of the composite laminate and the positive x-axis are defined as T0 and T1, respectively. This curve passes through the origin and is symmetrical about the origin. The expression for the angle between the curve and the positive x-axis is:

[0055]

[0056] in,

[0057] 'a' represents the length of the composite laminate along the x-axis, and the trajectory curve is marked as...<T0|T1> .

[0058] When T0 = T1, the composite laminate is formed by laying out strips in a straight line at equal intervals at a certain angle.

[0059] The slope of the centerline of the reference paving strip is:

[0060]

[0061] The reference trajectory for laying the center line is as follows:

[0062]

[0063] Maximum width of the laying strip:

[0064] W max =C···(4)

[0065] like Figure 3 As shown, the effective width Weff of the laying tape in the y direction is:

[0066]

[0067] Define the reference laying strip as laying strip 0, and let the coordinates of any point on the center line of laying strip 0 be (x0, y0). Then it satisfies equations (1)-(3), and thus:

[0068]

[0069]

[0070] Based on the centerline of the No. 0 laying strip, the centerlines of other laying strips are obtained by offsetting along the normal direction, which ensures that all laying strips are in an equal spacing relationship. This can effectively solve the defects of edge overlap and gap when laying the laying strips of each layer of composite laminate.

[0071] like Figure 4 As shown, any point P(x, y) within each layer of the composite laminate must lie on an equidistant curve of the centerline of layup strip 0. Let the distance between this equidistant curve and the centerline of layup strip 0 be d (defined as positive upwards and negative downwards), then the equation of the equidistant curve can be written as:

[0072]

[0073] Eliminating d yields a nonlinear equation for x0:

[0074] (x-x0)+(y-y0(x0))tan[θ(x0)]=0···(9)

[0075] Solving the above nonlinear equations, we can obtain the laying strip angle θ(P) = θ(x0) at point P.

[0076] The following formula can be used to determine that point P is located in paving strip k:

[0077]

[0078]

[0079] In the formula, floor() is for flooring down.

[0080] The solution method for nonlinear equation (9) can be found as follows:

[0081] Let g(x0) = (x - x0) + (y - y0(x0))tan[θ(x0)], then we have:

[0082] g'(x0)=(y-y0(x0))(1+tan 2 [θ(x0)])θ'(x0)-tan 2 [θ(x0)]-1···(12)

[0083] in,

[0084]

[0085] (1) Initialization:

[0086]

[0087] (2) Update: To avoid numerical divergence, the range of iterative values ​​is constrained:

[0088]

[0089]

[0090] In equations (15) and (16), λ and μ are random numbers between 0 and 1; TOL is the specified tolerance, which can be selected according to requirements, and TOL can be taken as 10. -4 ;

[0091] (3) Determine if Pick For the result calculated for x0, if Continue iterating.

[0092] The above methods and procedures can be programmed using Python and further combined with Abaqus simulation software to model composite laminates for computational analysis.

[0093] In one specific embodiment, the composite laminate has dimensions of 200mm × 200mm, and the maximum width W of the layup strip is... max =63.5mm, set the curve form as <30|60>, and determine the curve layup trajectory of each layer of the composite laminate using the method for determining the layup trajectory of each layer of the composite laminate disclosed in this application. The following steps can be referred to for implementation:

[0094] 1) Assuming T0 = 30° and T1 = 60°, according to formula (1), the angle between the centerline of the reference laying strip and the positive x-axis at each position can be obtained.

[0095] 2) Convert T0 and T1 to radians, and obtain the curve trajectory from formula (3): Based on this formula, the value of (x, y) at any point can be obtained, thus drawing the centerline of the reference paving strip. Any point (x0, y0) on the centerline of paving strip No. 0 satisfies:

[0096]

[0097] 3) Assuming point P is (10, 50), solve the nonlinear equation (9) according to formulas (12)-(16) to obtain... The value is 12.83. Substituting it into formula (6), we can obtain the laying angle of the corresponding laying strip at point P (10, 50). It is 33.85°;

[0098] 4) Substituting into formula (7), we can calculate the result. The value is 8.0. Substituting into formula (10) and formula (11), we get d = 42.1 and k = 1. That is, the point P(10, 50) is located in the first laying strip, and its corresponding laying strip angle is the same as the laying strip angle of point (12.83, 8.0) on the 0 laying strip, which is 33.85°.

[0099] The above process can be programmed using Python to divide the 200mm×200mm area into 1mm sections. 2 By dividing the area into square cells and using the coordinates of the center point of each cell for judgment, and traversing each cell, the distribution of the laying strip within the entire area can be obtained, as follows: Figure 5 The situation is shown below.

[0100] The various embodiments in the specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0101] The technical solution of this application has been described in conjunction with the preferred embodiments shown in the accompanying drawings. Those skilled in the art should understand that the scope of protection of this application is obviously not limited to these specific embodiments. Without departing from the principles of this application, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after these changes or substitutions will all fall within the scope of protection of this application.

Claims

1. A method for determining the layup trajectory of each layer of a composite laminate with a curved layup strip, characterized in that, include: Determine the reference layup strips for each layer of the composite laminate; Assume that the points on each layup strip of each layer of the composite laminate are equidistant from the centerline of its reference layup strip in the normal direction; Calculate the layup strip and its layup angle at each point within each layer of the composite laminate, and then obtain the curved layup trajectory of each layup strip. A linear angle layup method is used to define the centerline of the reference layup strip. A rectangular coordinate system is established at the center point of the composite laminate, with the x-axis horizontal and the y-axis vertical. The angle between the layup strip direction and the x-axis is defined as the layup angle. The centerline of the reference layup strip passes through the origin and is symmetrical about the origin. The angle between the tangent of the curve at the center of the reference layup strip and the positive x-axis is defined as... The angle between the tangent of the curve at the boundary of the reference laying strip centerline and the positive x-axis is: ; When T0=T1, each layer of the composite laminate is formed by laying out strips in parallel straight lines at equal intervals at a certain angle; Define the reference laying strip as laying strip 0. Based on the centerline of laying strip 0, offset along the normal direction to obtain the centerlines of other laying strips, ensuring that all laying strips are in an equidistant relationship. The calculation of the layup zone and its slope at each point within each layer of the composite laminate is specifically as follows: ； ； ； ； ； ； in, This refers to the number of the laying strip where each point is located within each layer of the composite laminate; This is the floor function; The distance from a point within each layer of the composite laminate along the normal direction to the centerline of the reference layup strip; This refers to the maximum width of the laying strip; The coordinates of points within the range of each layer of the composite laminate; The coordinates of the points on the center line of the reference paving strip; For reference, lay out the center point of the laying strip at the laying angle; The length of each layer of the composite laminate along the x-axis; The laying angle of the layup strip where a point is located within each layer of the composite laminate.

2. The method for determining the layup trajectory of each layer of the composite laminate according to claim 1, characterized in that, The determination of the reference layup strip for each layer of the composite laminate is specifically as follows: The composite laminate is laid out according to a set curve, with the centerline passing through the midpoint of each layer as a reference layout strip.

3. The method for determining the layup trajectory of each layer of the composite laminate according to claim 2, characterized in that, Solve using the following method: make ; ； ； ； exist At that time, take ; in, for The initial, nth, and (n+1)th iteration values ​​are calculated. A random number between 0 and 1; For tolerance; For intermediate calculation variables.

4. The method for determining the layup trajectory of each layer of the composite laminate according to claim 3, characterized in that, 。

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